Reference-free EPI Nyquist ghost correction using annihilating filter-based low rank hankel matrix for K-space interpolation

MR measurements from an EPI sequence produce Nyquist ghost artifacts that originate from inconsistencies between odd and even echoes. By converting the ghost correction problem to an interpolation problem from uniformly down-sampled even and odd phases, here we propose a single pass reference free ghost artifact removal algorithm. Specifically, our algorithm exploits an observation that the difference between the even and odd echoes is a Fourier transform of an underlying sparse image. Accordingly, we can construct a rank-deficient Hankel structured matrix in k-space, whose missing data can be recovered using recently proposed annihilating filter-based low rank Hankel structured matrix completion approach (ALOHA). The proposed method was applied to EPI data for both single and multi-coil acquisitions. Experimental results using in-vivo data confirmed that the proposed method can completely remove ghost artifacts successfully without any pre-scan data.